Question

已知/ab-2/与/b-1/互为相反数,试求代数式 1 1 1 1 —+ ---------- + ----------

Answer 1

/ab-2/与/b-1/互为相反数,则必都为0,则b=1,a=2

1/1*2+1/2*3+1/3*4+.+1/2010*2011=

1-1/2+1/2-1/3+1/3-1/4+1/2010-1/2011=1-1/2011=2010/2011